data dive week- 10

data <- read.csv ("C:\\Users\\91630\\OneDrive\\Desktop\\statistics\\age_gaps.CSV")

library(ggplot2)
library(ggthemes)

## Warning: package 'ggthemes' was built under R version 4.3.3

library(ggrepel)

## Warning: package 'ggrepel' was built under R version 4.3.3

library(boot)
library(broom)
library(lindia)

## Warning: package 'lindia' was built under R version 4.3.3

I am going to work on encoded_gender column.

data$encoded_gender <- ifelse(data$character_1_gender == "man", 0, 1)

I selected age_difference, release_year, actor_1_age, and couple_number as my explanatory variables.

model <- glm(encoded_gender ~ age_difference + release_year + actor_1_age + couple_number, data = data, family = binomial(link = 'logit'))

summary(model)

## 
## Call:
## glm(formula = encoded_gender ~ age_difference + release_year + 
##     actor_1_age + couple_number, family = binomial(link = "logit"), 
##     data = data)
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)    -30.999206  13.093538  -2.368   0.0179 *  
## age_difference  -0.135770   0.019006  -7.143  9.1e-13 ***
## release_year     0.015353   0.006555   2.342   0.0192 *  
## actor_1_age     -0.005824   0.010585  -0.550   0.5821    
## couple_number    0.035809   0.097700   0.367   0.7140    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1107.20  on 1154  degrees of freedom
## Residual deviance:  972.38  on 1150  degrees of freedom
## AIC: 982.38
## 
## Number of Fisher Scoring iterations: 6

Intersection: -30.999206

• This intercept shows that when all other predictor variables are zero, the log-odds of encoded_gender are one (woman).

• It is challenging to assess this value in its unprocessed state, though, because of how negative it is.

Age_difference (-0.135770):

• For every unit increase in age_difference, the log-odds of encoded_gender being 1 (woman) reduce by approximately 0.135770 when all other variables remain constant.

• This demonstrates that the likelihood of encoded_gender being 1 (woman) drops with increasing character age.

  Release Year (0.015353):

• Every unit increase in release_year raises the log-odds of encoded_gender being 1 (woman) by approximately 0.015353 when all other variables are maintained constant.

• This indicates that the likelihood of a recent film having encoded_gender = 1 (woman) is slightly higher.

  
  actor_1_age is -0.005824:

• For every unit increase in actor_1_age, the log-odds of encoded_gender being 1 (woman) fall by approximately 0.005824 when all other variables remain constant.

• This implies that there is a modest drop in the likelihood that encoded_gender will be 1 (woman) as actor 1 gets older.

  
  Couple number (0.035809):

• For every unit increase in couple_number, the log-odds of encoded_gender being 1 (woman) increase by approximately 0.035809 when all other variables stay constant.

• It shows that there is a tiny increase in the likelihood that movies with a higher couple_number (which may indicate a larger emphasis on or main romantic couples) will have encoded_gender 1 (woman).

Confidence interval for the “age_difference” coefficient:

coef_age_difference <- -0.135770
se_age_difference <- 0.019006

lower_bound <- coef_age_difference - 1.96 * se_age_difference
upper_bound <- coef_age_difference + 1.96 * se_age_difference

cat("95% Confidence Interval for the coefficient of age_difference: (", round(lower_bound, 3), ",", round(upper_bound, 3), ")\n")

## 95% Confidence Interval for the coefficient of age_difference: ( -0.173 , -0.099 )

• The log-odds of the encoded gender being 1 (woman) fall by an average of 0.135 units as the age difference between the characters grows by one unit.

• We have a 95% confidence level that an accurate decrease in log-odds between 0.098 and 0.173 units occurs for every unit increase in age difference.

• This indicates that, given a 95% confidence level that the reduction falls within the designated range, the likelihood of the character being decoded as a woman (1) drops as the characters’ ages get closer together.The log-odds of the encoded gender being 1 (woman) fall by an average of 0.135 units as the age difference between the characters grows by one unit.

• We have a 95% confidence level that an accurate decrease in log-odds between 0.098 and 0.173 units occurs for every unit increase in age difference.

• This indicates that, given a 95% confidence level that the reduction falls within the designated range, the likelihood of the character being decoded as a woman (1) drops as the characters’ ages get closer together.

Plotting the age_difference coefficient’s confidence interval:

confidence_interval <- data.frame(
  coefficient = "age_difference",
  estimate = coef_age_difference,
  lower = lower_bound,
  upper = upper_bound
)

ggplot(confidence_interval, aes(x = coefficient, y = estimate)) +
  geom_bar(stat = "identity", fill = "pink", width = 0.5) +
  geom_errorbar(aes(ymin = lower, ymax = upper), width = 0.2, color = "purple") +
  labs(title = "95% Confidence Interval for Coefficient of age_difference",
       x = "Coefficient",
       y = "Estimate") +
  coord_flip() +
  theme_minimal()